One of the interesting things about Facebook is that, of the interesting pages on Facebook, everyone sees a different version of that page.
Search is clearly filtered to show stuff that is more relevant to you first. Your ‘facebook’ page has stuff filtered out depending on what Facebook thinks is interesting to you (with input from the tiny ‘Preferences’ settings that I expect no-one actually changes)
Search is the tricky one. If someone tells you to type something into Google, you’ll see the same results as them. On Facebook, probably not! This could give Facebook great opportunities for advertising, but their search actually sucks! e.g. I searched for an app the other day and couldn’t find it – I was using the singular form of the name when I should have used the plural. Now I have that app installed, it shows up higher in the search, but now it’s too late.